Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:

import java.util.*;

public class Main {

    
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        
        HashSet<Long> set = new HashSet<Long>();
        
        long k = 1;
        while(true){
            long t = k*(k+1)/2;
            if(t>=1000000000)
                break;
            set.add(t);
            k++;
        }
//      System.out.println(set.size());
        long n = s.nextLong();
        
        int ok = 0;
        for(long a:set){
            long b = n - a;
            if(set.contains(b)){
                ok = 1;
                break;
            }
        }
        if(ok==1)
            System.out.println("YES");
        else System.out.println("NO");
    }

}